What is the solution for (dy)/(dx)=sin(x+y)+cos(x+y) ?

The solution for (dy)/(dx)=sin(x+y)+cos(x+y) is y=2arctan(e^{x+c_{1}}-1)+2pin-x

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(dy)/(dx)=sin(x+y)+cos(x+y)

\frac{d y}{d x} = sin (x + y) + cos (x + y)

y = 2 arctan (e^{x + c_{1}} - 1) + 2 πn - x

Solution steps

\frac{d y}{d x} = sin (x + y) + cos (x + y)

Solve using substitution:

y = 2 arctan (e^{x + c_{1}} - 1) + 2 πn - x

y = 2 arctan (e^{x + c_{1}} - 1) + 2 πn - x

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What is the solution for (dy)/(dx)=sin(x+y)+cos(x+y) ?
The solution for (dy)/(dx)=sin(x+y)+cos(x+y) is y=2arctan(e^{x+c_{1}}-1)+2pin-x